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Chapter 6: Q.6.1 (page 367)

What is the z-score of x, when x=1and X~N(12,3)?

Short Answer

Expert verified

The value of the z-score for x=1isrole="math" localid="1648286217464" -3.67.

Step by step solution

01

Given Information

x=1andX~N(12,3).

02

Explanation

μ=12

σ=3

Now, the z-score for x=1can be calculated as below:

z-score=1-μσ

=1-123

=-113

=-3.67.

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Most popular questions from this chapter

Use the following information to answer the next four exercises:

X~N(54,8)

Find the probability thatx>56.

Define the random variable X in words. X = _______________.

Kyle’s doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ=125and standard deviation σ=14. If X = a systolic blood pressure score then X~N(125,14).

a. Which answer(s) is/are correct?

  1. Kyle’s systolic blood pressure is 175.
  2. Kyle’s systolic blood pressure is 1.75times the average blood pressure of men his age.
  3. Kyle’s systolic blood pressure is 1.75above the average systolic blood pressure of men his age. i
  4. Kyles’s systolic blood pressure is1.75 standard deviations above the average systolic blood pressure for men.

b. Calculate Kyle’s blood pressure.

About what percent of x values lie between the first and third standard deviations(both sides)?

In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.
See all solutions

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